Damir Filipović

Ecole Polytechnique Fédérale de Lausanne (EPFL) - Swiss Finance Institute (SFI)

Title

Kernel Density Machines

Authors

Damir Filipović and Paul Schneider

Abstract

We introduce Kernel Density Machines (KDM), a nonparametric framework for estimating the Radon-Nikodym derivative between two probability measures from which samples can be drawn. This flexible and powerful approach enables a broad range of applications, including independence testing and the estimation of multivariate conditional distributions. Leveraging a low-rank kernel approximation with sharply controlled approximation error, KDM is both computationally efficient and scalable to very large datasets. We provide a comprehensive set of theoretical results, including asymptotic consistency and finite-sample guarantees, offering rigorous performance bounds and insights into the framework's effectiveness across diverse applications.